Bilinear Input Modulation for Mamba: Koopman Bilinear Forms for Memory Retention and Multiplicative Computation
Selective State Space Models (SSMs), notably Mamba, employ diagonal state transitions that limit both memory retention and bilinear computational capacity. We propose a factorized bilinear input modulation that augments the SSM with a state-input product, interpretable as a finite-dimensional Koopman bilinear form. After introducing a shared state across channels (Coupled SSM), the modulation admits three implementations. Coupled Bilinear Input Modulation (seq-BIM) retains the full bilinear product on the input side at the cost of sequential computation, Coupled Gated Modulation (GM) linearizes it into a gate modulation that is compatible with the parallel scan, and Parallel Bilinear Inpu...
| Authors | Hiroki Fujii, Masaki Yamakita |
|---|---|
| Primary category | eess.SY |
| Published | 19 April 2026 |
| Last updated at source | 26 April 2026 |
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